I tried to find the answer to this question in the rules book but it doesn't really say.

Under Fleeing the Battlefield in the Rules Reference, pg. 11: (There is a bit more there, but this sums it up. ANY PART bolded and uppercase for emphasis)

Also worth noting that feeing the battlefield prevents triggering of any abilities that might be triggered upon the death of the ship, including but not limited to undocking docked ships, triggering 'when you are/would be destroyed' abilities such as Dead Man's Switch or Tel Trevura's pilot ability.

So you can't just suicide your Z95 off the side of the board next to a low-health ship in order to trigger Dead Man's Switch.

If you land with any part of the base off the board you have left the area and are now dead.

I say "land" because you can have your templates go off of the edge (most likely a hard turn) but have the ship land back in the field of play and be safe.

Under Fleeing the Battlefield in the Rules Reference, pg. 11: (There is a bit more there, but this sums it up. ANY PART bolded and uppercase for emphasis)

When a ship executes a maneuver or performs an

action that changes its position, if ANY PART of

its base is outside the play area, that ship has fled

the battlefield. A ship that flees the battlefield is

destroyed.

Remember it is only the final position of the ship that matters, nothing else. It does not travel along the template, it is moved from one end to the other. Also, you can not boost or barrell roll off the battlefield; those are illegal moves and you would need to try a different direction or take another action or even do no action.

Note that the "or performs an action that changes its position" text is currently obsolete (or future-proofing), since Boost and Barrel Roll no longer allow you to flee the battlefield.

What about BR or boost back onto the playing area?

I have missed judged the remove during a bank maneuver (should of used hard turn) and now a portion of a ship is off the play area. Can that ship then boost or barrel roll to get back?

What about BR or boost back onto the playing area?

I have missed judged the remove during a bank maneuver (should of used hard turn) and now a portion of a ship is off the play area. Can that ship then boost or barrel roll to get back?

No, it can't. As soon as the ship lands off the board, it's destroyed. It doesn't get its Perform Action step, so there's no option to barrel roll or boost back onto the board.